Problem 1
During dinner hour, distribution of inter-arrival time of customers at Burger Barn is computed as follows:
Inter-arrival Time Probability
30 seconds .45
60 seconds .25
90 seconds .15
120 seconds .10
150 seconds .05
Sixty percent of customers pay with cash, while 40% pay with credit cards.
Payment Method Probability
Cash .60
Credit .40
Service time of the cash and credit card customers are estimated to be as follows:
Cash Credit Card
Service Time Probability Service Time Probability
20 seconds .35 30 seconds .20
40 seconds .30 60 seconds .45
60 seconds .25 90 seconds .25
80 seconds .10 120 seconds .10
Simulate this system for 20 customer arrivals and find out the average time a cash and credit card customer should wait in line before paying cashier. Use random numbers in table below to find out the customer inter-arrival time, whether customer pays with cash or credit, the service time.
You would be working with three probabilistic variables, inter-arrival time, payment method and the service time. Also utilze excel template attached when solving this problem.
Random Numbers
Inter-arrival Time Payment Method Service Time
63 10 19
46 73 79
86 28 35
0 51 63
56 91 54
67 14 51
59 64 93
28 24 69
79 70 14
64 84 35
33 73 1
81 17 9
17 48 70
63 11 50
66 88 40
27 94 41
4 29 71
34 83 68
7 71 50
69 27 82